Mathematical Modeling of Hydroelastic Interaction Between Stamp and Three-Layered Beam Resting on Winkler Foundation

Abstract

The purpose of the article is to develop the mathematical model of bending oscillations of a three-layered beam, resting in Winkler foundation and interacting with a vibrating stamp through a thin layer of viscous incompressible liquid. The three-layered beam with incompressible lightweight filler by using broken normal hypothesis was considered. The bending oscillations equation of three-layered beam resting on Winkler foundation and interacting with vibrating stamp through viscous liquid layer is obtained. On the basis of plane hydroelasticity problem solution, the laws of the three-layered beam deflections and pressure in the liquid along the channel are found. The frequency dependent functions of the beam deflections amplitude distribution and liquid pressure along the channel are constructed. The obtained results allow to define oscillations resonance frequencies and to study tense-deformed state of three-layered beam, as well as, hydrodynamic parameters of viscous liquid interacting with vibrating stamp and three-layered beam, resting on Winkler foundation. The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 19-01-00014-a.